### Evaluate the Integral #### Problem Statement: Evaluate the integral: \[ \int \frac{5x + 8}{x^3 + x} \, dx \] #### Answer Choices: a. \( 8\ln x + 5\tan^{-1} x + C \) b. \( \frac{-4}{x^2} - \frac{5}{x} + C \) c. \( 4\ln x + 5\tan^{-1} x - 8\ln(x^2 + 1) + C \) d. \( 8\ln x + 5\tan^{-1} x - 4\ln(x^2 + 1) + C \) e. \( 8\ln x - \tan^{-1} x - 4\ln(x^2 + 1) + C \) In this problem, you are required to evaluate the integral given and choose the correct answer from the provided options. The correct answer is marked with a purple circle.
### Evaluate the Integral #### Problem Statement: Evaluate the integral: \[ \int \frac{5x + 8}{x^3 + x} \, dx \] #### Answer Choices: a. \( 8\ln x + 5\tan^{-1} x + C \) b. \( \frac{-4}{x^2} - \frac{5}{x} + C \) c. \( 4\ln x + 5\tan^{-1} x - 8\ln(x^2 + 1) + C \) d. \( 8\ln x + 5\tan^{-1} x - 4\ln(x^2 + 1) + C \) e. \( 8\ln x - \tan^{-1} x - 4\ln(x^2 + 1) + C \) In this problem, you are required to evaluate the integral given and choose the correct answer from the provided options. The correct answer is marked with a purple circle.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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![### Evaluate the Integral
#### Problem Statement:
Evaluate the integral:
\[ \int \frac{5x + 8}{x^3 + x} \, dx \]
#### Answer Choices:
a. \( 8\ln x + 5\tan^{-1} x + C \)
b. \( \frac{-4}{x^2} - \frac{5}{x} + C \)
c. \( 4\ln x + 5\tan^{-1} x - 8\ln(x^2 + 1) + C \)
d. \( 8\ln x + 5\tan^{-1} x - 4\ln(x^2 + 1) + C \)
e. \( 8\ln x - \tan^{-1} x - 4\ln(x^2 + 1) + C \)
In this problem, you are required to evaluate the integral given and choose the correct answer from the provided options. The correct answer is marked with a purple circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d8d0c97-e66d-424a-9c52-d4c7d8464ad8%2F9aa15741-f61e-4b03-9428-60e84157e17d%2Fmebz1sa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluate the Integral
#### Problem Statement:
Evaluate the integral:
\[ \int \frac{5x + 8}{x^3 + x} \, dx \]
#### Answer Choices:
a. \( 8\ln x + 5\tan^{-1} x + C \)
b. \( \frac{-4}{x^2} - \frac{5}{x} + C \)
c. \( 4\ln x + 5\tan^{-1} x - 8\ln(x^2 + 1) + C \)
d. \( 8\ln x + 5\tan^{-1} x - 4\ln(x^2 + 1) + C \)
e. \( 8\ln x - \tan^{-1} x - 4\ln(x^2 + 1) + C \)
In this problem, you are required to evaluate the integral given and choose the correct answer from the provided options. The correct answer is marked with a purple circle.
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